
These expressions, which parameterize the influence of the rectangular lattice via \(a\) , are simpler than those presented in Ref. [1]} due to the use of non-orthogonal moment basis and the construction of the equilibria directly from the Maxwell distribution function via matching without the use of free parameters in this work. Based on these and performing simulations by considering the fluid to be initially at rest, Fig. REF  presents the instantaneous velocity profiles \(u(y,t)\)  computed using the RNR-LBM and RC-LBM at various dimensionless time instants \(T\)  of 2, 5, 10, 20 and 40, along with the analytical solution plotted at all these time instants. Very good agreement between the two rectangular LB schemes and the time-dependent analytical solution are found. The temporal development of the velocity field leading to a steady state linear profile is well reproduced by both RNR-LBM and RC-LBM.
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